The Bears were in the endzone again six minutes into the second quarter, as McCown ran down the middle and juked a defender before leaping over the line for a seven-yard score.
Chicago's lead lasted just 216 seconds before Romo faked the handoff on third and one to feed the ball to Jason Witten, who powered through a couple of tackles to reach the endzone.
However, the hosts were in front again 94 seconds before half time when Robbie Gould made a 27-yard field goal.
Alshon Jeffery then extended the Bears' lead to 10 points by making a superb grab under pressure for a 25-yard score with the final play of the second quarter.
After play resumed, Gould kicked a 34-yard field goal before Matt Forte collected a McCown pass and ran into the endzone from the one-yard line. Forte's touchdown was followed by a two-point conversion.
Michael Bush capitalised on some tired Cowboys defense to touch down and make it 42-14 early in the fourth.
Cole Beasley then ended Chicago's 28-point streak by grabbing Romo's nine-yard pass in the endzone.
Another Gould field goal soon followed, but the Cowboys ended the game on a high as Joseph Randle powered through the middle of the line for a one-yard touchdown.